Abstract

Various types of background signals appear when wavelength-modulated (WM) diode-laser light is frequency doubled. We present a theoretical analysis of such background signals in terms of a previously derived formalism for WM spectrometry that is based on a Fourier series. Explicit expressions for various nf harmonics of the background signals are derived. The analysis shows that 2f detection will be plagued by significant background signals when frequency-doubled WM diode-laser light is used. It also demonstrates that 4f and 6f detection will experience background signals but not, however, to the same extent as 2f detection. The analysis illustrates clearly how the various nf harmonics of the background signals depend on entities such as modulation amplitude, associated intensity modulation, dispersion of the frequency-doubling material, laser power, and detuning. The background signals can take both positive and negative values, depending on the relation between these entities. Guidelines for how to minimize these background signals are given.

© 2001 Optical Society of America

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    [CrossRef] [PubMed]
  2. J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
    [CrossRef]
  3. D. T. Cassidy, J. Reid, “Atmospheric pressure monitoring of trace gases using tunable diode lasers,” Appl. Opt. 21, 1185–1190 (1982).
    [CrossRef] [PubMed]
  4. J. A. Silver, “Frequency-modulation spectroscopy for trace species detection: theory and comparison among experimental methods,” Appl. Opt. 31, 707–717 (1992).
    [CrossRef] [PubMed]
  5. A. Zybin, C. Schnürer-Patschan, K. Niemax, “Measurements of C2F4Cl2, CCl4, CHF3, and O2 by wavelength modulated laser absorption spectroscopy of excited Cl, F, and O in a DC discharge applying semiconductor diode lasers,” Spectrochim. Acta Part B 48, 1713–1718 (1993).
    [CrossRef]
  6. L. C. Philippe, R. K. Hanson, “Laser diode wavelength-modulation spectroscopy for simultaneous measurement of temperature, pressure, and velocity in shock-heated oxygen flows,” Appl. Opt. 32, 6090–6103 (1993).
    [CrossRef] [PubMed]
  7. C. Schnürer-Patschan, A. Zybin, H. Groll, K. Niemax, “Improvement in detection limit in graphite furnace diode laser atomic absorption spectrometry by wavelength modulation technique.” J. Anal. At. Spectrom. 8, 1103–1107 (1993).
    [CrossRef]
  8. J. M. Supplee, E. A. Whittaker, W. Lenth, “Theoretical description of frequency-modulation and wavelength-modulation spectroscopy,” Appl. Opt. 33, 6294–6302 (1994).
    [CrossRef] [PubMed]
  9. H. Groll, C. Schnürer-Patschan, Y. Kuritsyn, K. Niemax, “Wavelength modulation diode laser atomic absorption spectrometry in analytical flames,” Spectrochim. Acta Part B 49, 1463–1472 (1994).
    [CrossRef]
  10. A. Zybin, C. Schnürer-Patschan, K. Niemax, “Wavelength modulation diode laser atomic spectrometry in modulated low-pressure helium plasmas for element-selective detection in gas chromatography.” J. Anal. At. Spectrom. 10, 563–567 (1995).
    [CrossRef]
  11. C. Schnürer-Patschan, K. Niemax, “Elemental selective detection of chlorine in capillary gas chromatography by wavelength modulation diode laser atomic absorption spectrometry in a microwave induced plasma,” Spectrochim. Acta Part B 50, 963–969 (1995).
    [CrossRef]
  12. H. Groll, G. Schaldach, H. Berndt, K. Niemax, “Measurement of Cr(III)/Cr(VI) species by wavelength modulation diode laser flame atomic absorption spectrometry,” Spectrochim. Acta Part B 50, 1293–1298 (1995).
    [CrossRef]
  13. P. Werle, “Spectroscopic trace gas analysis using semiconductor diode lasers,” Spectrochim. Acta Part A 52, 805–822 (1996).
    [CrossRef]
  14. P. Ljung, O. Axner, “Measurements of rubidium in standard reference samples by wavelength-modulation diode laser spectrometry in graphite furnace,” Spectrochim. Acta Part B 52, 305–319 (1997).
    [CrossRef]
  15. N. Hadgu, J. Gustafsson, W. Frech, O. Axner, “Rubidium atom distribution and nonspectral interference effects in transversely heated graphite atomizers evaluated by wavelength modulated diode laser absorption spectrometry,” Spectrochim. Acta Part B 53, 923–943 (1998).
    [CrossRef]
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    [CrossRef]
  18. D. T. Cassidy, J. Reid, “Harmonic detection with tunable diode lasers—two-tone modulation,” Appl. Phys. B 29, 279–285 (1982).
    [CrossRef]
  19. D. S. Bomse, A. C. Stanton, J. A. Silver, “Frequency modulation and wavelength modulation spectroscopies: comparison of experimental methods using a lead-salt diode laser,” Appl. Opt. 31, 718–731 (1992).
    [CrossRef] [PubMed]
  20. J. A. Silver, A. C. Stanton, “Optical interference fringe reduction in laser absorption experiments,” Appl. Opt. 27, 1914–1916 (1988).
    [CrossRef] [PubMed]
  21. P. V. Cvijin, W. K. Wells, D. A. Gilmore, J. Wu, D. M. Hunten, G. H. Atkinson, “Fringe pattern suppression in intracavity laser spectroscopy,” Appl. Opt. 31, 5779–5784 (1992).
    [CrossRef] [PubMed]
  22. T. A. Hu, E. L. Chappell, J. T. Munley, S. W. Sharpe, “Improved multipass optics for diode-laser spectroscopy,” Rev. Sci. Instrum. 64, 3380–3383 (1993).
    [CrossRef]
  23. C. R. Webster, “Brewster-plate spoiler: a novel method for reducing the amplitude of interference fringes that limit tunable-laser absorption sensitivities,” J. Opt. Soc. Am. B 2, 1464–1470 (1985).
    [CrossRef]
  24. H. Ahlberg, S. Lundqvist, M. S. Schumate, U. Persson, “Analysis of errors caused by optical interference effects in wavelength-diverse CO2 laser long-path systems,” Appl. Opt. 24, 3917–3923 (1985).
    [CrossRef]
  25. L.-G. Wang, H. Riris, C. B. Carlisle, T. F. Gallagher, “Comparison of approaches to modulation spectroscopy with GaAlAs semiconductor lasers: application to water vapor,” Appl. Opt. 27, 2071–2077 (1988).
    [CrossRef] [PubMed]
  26. J. Reid, M. El-Sherbiny, B. K. Garside, E. A. Ballik, “Sensitivity limit of a tunable diode laser spectrometer, with application to the detection of NO2 at the 100-ppt level,” Appl. Opt. 19, 3349–3354 (1980).
    [CrossRef] [PubMed]
  27. N.-Y. Chou, G. W. Sachse, L.-G. Wang, T. F. Gallagher, “Optical fringe reduction technique for FM laser spectroscopy,” Appl. Opt. 28, 4973–4975 (1989).
    [CrossRef] [PubMed]
  28. T. Igushi, “Modulation waveforms for second-harmonic detection with tunable diode lasers,” J. Opt. Soc. Am. B 3, 419–423 (1986).
    [CrossRef]
  29. N. Kagawa, O. Wada, R. Koga, “Suppression of the etalon fringe in absorption spectrometry with an infrared tunable diode laser,” Opt. Eng. 36, 2586–2592 (1997).
    [CrossRef]
  30. P. Kluczynski, Å. M. Lindberg, O. Axner, “Characterization of background signals in wavelength-modulation spectrometry in terms of a Fourier based theoretical formalism,” Appl. Opt. 40, 770–782 (2001).
    [CrossRef]
  31. X. Zhu, D. T. Cassidy, “Modulation spectroscopy with a semiconductor diode laser by injection-current modulation,” J. Opt. Soc. Am. B 14, 1945–1950 (1997).
    [CrossRef]
  32. P. Kluczynski, O. Axner, “Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals,” Appl. Opt. 38, 5803–5815 (1999).
    [CrossRef]
  33. O. Axner, P. Kluczynski, Å. M. Lindberg, “A general noncomplex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function,” J. Quantum Spectrosc. Radiat. Transfer 68, 299–317 (2001).
    [CrossRef]
  34. P. Kluczynski, Å. M. Lindberg, O. Axner, “Background signals in wavelength-modulation spectrometry by use of frequency-doubled diode-laser light. II. Experiment,” Appl. Opt. 40, 794–805 (2001).
    [CrossRef]
  35. In deriving Eqs. (1) and (2), we made use of the fact that all odd transmission coefficients are zero, which follows from our choice of reference phase.
  36. Cζ is, in fact, frequency dependent but can, in the interval of frequency over which Eq. (15) takes any appreciable value, be considered constant.
  37. G. V. H. Wilson, “Modulation broadening of NMR and ESR lineshapes,” J. Appl. Phys. 34, 3276–3285 (1963).
    [CrossRef]

2001

1999

1998

N. Hadgu, J. Gustafsson, W. Frech, O. Axner, “Rubidium atom distribution and nonspectral interference effects in transversely heated graphite atomizers evaluated by wavelength modulated diode laser absorption spectrometry,” Spectrochim. Acta Part B 53, 923–943 (1998).
[CrossRef]

1997

P. Ljung, O. Axner, “Measurements of rubidium in standard reference samples by wavelength-modulation diode laser spectrometry in graphite furnace,” Spectrochim. Acta Part B 52, 305–319 (1997).
[CrossRef]

V. Liger, A. Zybin, Y. Kuritsyn, K. Niemax, “Diode-laser atomic-absorption spectrometry by the double-beam–double-modulation technique,” Spectrochim. Acta Part B 52, 1125–1138 (1997).
[CrossRef]

N. Kagawa, O. Wada, R. Koga, “Suppression of the etalon fringe in absorption spectrometry with an infrared tunable diode laser,” Opt. Eng. 36, 2586–2592 (1997).
[CrossRef]

X. Zhu, D. T. Cassidy, “Modulation spectroscopy with a semiconductor diode laser by injection-current modulation,” J. Opt. Soc. Am. B 14, 1945–1950 (1997).
[CrossRef]

1996

P. Werle, “Spectroscopic trace gas analysis using semiconductor diode lasers,” Spectrochim. Acta Part A 52, 805–822 (1996).
[CrossRef]

1995

A. Zybin, C. Schnürer-Patschan, K. Niemax, “Wavelength modulation diode laser atomic spectrometry in modulated low-pressure helium plasmas for element-selective detection in gas chromatography.” J. Anal. At. Spectrom. 10, 563–567 (1995).
[CrossRef]

C. Schnürer-Patschan, K. Niemax, “Elemental selective detection of chlorine in capillary gas chromatography by wavelength modulation diode laser atomic absorption spectrometry in a microwave induced plasma,” Spectrochim. Acta Part B 50, 963–969 (1995).
[CrossRef]

H. Groll, G. Schaldach, H. Berndt, K. Niemax, “Measurement of Cr(III)/Cr(VI) species by wavelength modulation diode laser flame atomic absorption spectrometry,” Spectrochim. Acta Part B 50, 1293–1298 (1995).
[CrossRef]

1994

H. Groll, C. Schnürer-Patschan, Y. Kuritsyn, K. Niemax, “Wavelength modulation diode laser atomic absorption spectrometry in analytical flames,” Spectrochim. Acta Part B 49, 1463–1472 (1994).
[CrossRef]

J. M. Supplee, E. A. Whittaker, W. Lenth, “Theoretical description of frequency-modulation and wavelength-modulation spectroscopy,” Appl. Opt. 33, 6294–6302 (1994).
[CrossRef] [PubMed]

1993

L. C. Philippe, R. K. Hanson, “Laser diode wavelength-modulation spectroscopy for simultaneous measurement of temperature, pressure, and velocity in shock-heated oxygen flows,” Appl. Opt. 32, 6090–6103 (1993).
[CrossRef] [PubMed]

A. Zybin, C. Schnürer-Patschan, K. Niemax, “Measurements of C2F4Cl2, CCl4, CHF3, and O2 by wavelength modulated laser absorption spectroscopy of excited Cl, F, and O in a DC discharge applying semiconductor diode lasers,” Spectrochim. Acta Part B 48, 1713–1718 (1993).
[CrossRef]

C. Schnürer-Patschan, A. Zybin, H. Groll, K. Niemax, “Improvement in detection limit in graphite furnace diode laser atomic absorption spectrometry by wavelength modulation technique.” J. Anal. At. Spectrom. 8, 1103–1107 (1993).
[CrossRef]

T. A. Hu, E. L. Chappell, J. T. Munley, S. W. Sharpe, “Improved multipass optics for diode-laser spectroscopy,” Rev. Sci. Instrum. 64, 3380–3383 (1993).
[CrossRef]

1992

1989

1988

1986

1985

1982

D. T. Cassidy, J. Reid, “Harmonic detection with tunable diode lasers—two-tone modulation,” Appl. Phys. B 29, 279–285 (1982).
[CrossRef]

D. T. Cassidy, J. Reid, “Atmospheric pressure monitoring of trace gases using tunable diode lasers,” Appl. Opt. 21, 1185–1190 (1982).
[CrossRef] [PubMed]

1981

J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

1980

1977

1963

G. V. H. Wilson, “Modulation broadening of NMR and ESR lineshapes,” J. Appl. Phys. 34, 3276–3285 (1963).
[CrossRef]

Ahlberg, H.

Atkinson, G. H.

Axner, O.

P. Kluczynski, Å. M. Lindberg, O. Axner, “Characterization of background signals in wavelength-modulation spectrometry in terms of a Fourier based theoretical formalism,” Appl. Opt. 40, 770–782 (2001).
[CrossRef]

O. Axner, P. Kluczynski, Å. M. Lindberg, “A general noncomplex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function,” J. Quantum Spectrosc. Radiat. Transfer 68, 299–317 (2001).
[CrossRef]

P. Kluczynski, Å. M. Lindberg, O. Axner, “Background signals in wavelength-modulation spectrometry by use of frequency-doubled diode-laser light. II. Experiment,” Appl. Opt. 40, 794–805 (2001).
[CrossRef]

P. Kluczynski, O. Axner, “Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals,” Appl. Opt. 38, 5803–5815 (1999).
[CrossRef]

N. Hadgu, J. Gustafsson, W. Frech, O. Axner, “Rubidium atom distribution and nonspectral interference effects in transversely heated graphite atomizers evaluated by wavelength modulated diode laser absorption spectrometry,” Spectrochim. Acta Part B 53, 923–943 (1998).
[CrossRef]

P. Ljung, O. Axner, “Measurements of rubidium in standard reference samples by wavelength-modulation diode laser spectrometry in graphite furnace,” Spectrochim. Acta Part B 52, 305–319 (1997).
[CrossRef]

Ballik, E. A.

Berndt, H.

H. Groll, G. Schaldach, H. Berndt, K. Niemax, “Measurement of Cr(III)/Cr(VI) species by wavelength modulation diode laser flame atomic absorption spectrometry,” Spectrochim. Acta Part B 50, 1293–1298 (1995).
[CrossRef]

Bomse, D. S.

Carlisle, C. B.

Cassidy, D. T.

Chappell, E. L.

T. A. Hu, E. L. Chappell, J. T. Munley, S. W. Sharpe, “Improved multipass optics for diode-laser spectroscopy,” Rev. Sci. Instrum. 64, 3380–3383 (1993).
[CrossRef]

Chou, N.-Y.

Cvijin, P. V.

El-Sherbiny, M.

Frech, W.

N. Hadgu, J. Gustafsson, W. Frech, O. Axner, “Rubidium atom distribution and nonspectral interference effects in transversely heated graphite atomizers evaluated by wavelength modulated diode laser absorption spectrometry,” Spectrochim. Acta Part B 53, 923–943 (1998).
[CrossRef]

Gallagher, T. F.

Garside, B. K.

Gilmore, D. A.

Groll, H.

H. Groll, G. Schaldach, H. Berndt, K. Niemax, “Measurement of Cr(III)/Cr(VI) species by wavelength modulation diode laser flame atomic absorption spectrometry,” Spectrochim. Acta Part B 50, 1293–1298 (1995).
[CrossRef]

H. Groll, C. Schnürer-Patschan, Y. Kuritsyn, K. Niemax, “Wavelength modulation diode laser atomic absorption spectrometry in analytical flames,” Spectrochim. Acta Part B 49, 1463–1472 (1994).
[CrossRef]

C. Schnürer-Patschan, A. Zybin, H. Groll, K. Niemax, “Improvement in detection limit in graphite furnace diode laser atomic absorption spectrometry by wavelength modulation technique.” J. Anal. At. Spectrom. 8, 1103–1107 (1993).
[CrossRef]

Gustafsson, J.

N. Hadgu, J. Gustafsson, W. Frech, O. Axner, “Rubidium atom distribution and nonspectral interference effects in transversely heated graphite atomizers evaluated by wavelength modulated diode laser absorption spectrometry,” Spectrochim. Acta Part B 53, 923–943 (1998).
[CrossRef]

Hadgu, N.

N. Hadgu, J. Gustafsson, W. Frech, O. Axner, “Rubidium atom distribution and nonspectral interference effects in transversely heated graphite atomizers evaluated by wavelength modulated diode laser absorption spectrometry,” Spectrochim. Acta Part B 53, 923–943 (1998).
[CrossRef]

Hanson, R. K.

Hu, T. A.

T. A. Hu, E. L. Chappell, J. T. Munley, S. W. Sharpe, “Improved multipass optics for diode-laser spectroscopy,” Rev. Sci. Instrum. 64, 3380–3383 (1993).
[CrossRef]

Hunten, D. M.

Igushi, T.

Kagawa, N.

N. Kagawa, O. Wada, R. Koga, “Suppression of the etalon fringe in absorption spectrometry with an infrared tunable diode laser,” Opt. Eng. 36, 2586–2592 (1997).
[CrossRef]

Kluczynski, P.

Koga, R.

N. Kagawa, O. Wada, R. Koga, “Suppression of the etalon fringe in absorption spectrometry with an infrared tunable diode laser,” Opt. Eng. 36, 2586–2592 (1997).
[CrossRef]

Kuritsyn, Y.

V. Liger, A. Zybin, Y. Kuritsyn, K. Niemax, “Diode-laser atomic-absorption spectrometry by the double-beam–double-modulation technique,” Spectrochim. Acta Part B 52, 1125–1138 (1997).
[CrossRef]

H. Groll, C. Schnürer-Patschan, Y. Kuritsyn, K. Niemax, “Wavelength modulation diode laser atomic absorption spectrometry in analytical flames,” Spectrochim. Acta Part B 49, 1463–1472 (1994).
[CrossRef]

Labrie, D.

J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

Lenth, W.

Liger, V.

V. Liger, A. Zybin, Y. Kuritsyn, K. Niemax, “Diode-laser atomic-absorption spectrometry by the double-beam–double-modulation technique,” Spectrochim. Acta Part B 52, 1125–1138 (1997).
[CrossRef]

Lindberg, Å. M.

Ljung, P.

P. Ljung, O. Axner, “Measurements of rubidium in standard reference samples by wavelength-modulation diode laser spectrometry in graphite furnace,” Spectrochim. Acta Part B 52, 305–319 (1997).
[CrossRef]

Lundqvist, S.

Moses, E. I.

Munley, J. T.

T. A. Hu, E. L. Chappell, J. T. Munley, S. W. Sharpe, “Improved multipass optics for diode-laser spectroscopy,” Rev. Sci. Instrum. 64, 3380–3383 (1993).
[CrossRef]

Niemax, K.

V. Liger, A. Zybin, Y. Kuritsyn, K. Niemax, “Diode-laser atomic-absorption spectrometry by the double-beam–double-modulation technique,” Spectrochim. Acta Part B 52, 1125–1138 (1997).
[CrossRef]

A. Zybin, C. Schnürer-Patschan, K. Niemax, “Wavelength modulation diode laser atomic spectrometry in modulated low-pressure helium plasmas for element-selective detection in gas chromatography.” J. Anal. At. Spectrom. 10, 563–567 (1995).
[CrossRef]

C. Schnürer-Patschan, K. Niemax, “Elemental selective detection of chlorine in capillary gas chromatography by wavelength modulation diode laser atomic absorption spectrometry in a microwave induced plasma,” Spectrochim. Acta Part B 50, 963–969 (1995).
[CrossRef]

H. Groll, G. Schaldach, H. Berndt, K. Niemax, “Measurement of Cr(III)/Cr(VI) species by wavelength modulation diode laser flame atomic absorption spectrometry,” Spectrochim. Acta Part B 50, 1293–1298 (1995).
[CrossRef]

H. Groll, C. Schnürer-Patschan, Y. Kuritsyn, K. Niemax, “Wavelength modulation diode laser atomic absorption spectrometry in analytical flames,” Spectrochim. Acta Part B 49, 1463–1472 (1994).
[CrossRef]

C. Schnürer-Patschan, A. Zybin, H. Groll, K. Niemax, “Improvement in detection limit in graphite furnace diode laser atomic absorption spectrometry by wavelength modulation technique.” J. Anal. At. Spectrom. 8, 1103–1107 (1993).
[CrossRef]

A. Zybin, C. Schnürer-Patschan, K. Niemax, “Measurements of C2F4Cl2, CCl4, CHF3, and O2 by wavelength modulated laser absorption spectroscopy of excited Cl, F, and O in a DC discharge applying semiconductor diode lasers,” Spectrochim. Acta Part B 48, 1713–1718 (1993).
[CrossRef]

Oh, D. B.

Persson, U.

Peterson, K. A.

Philippe, L. C.

Reid, J.

D. T. Cassidy, J. Reid, “Harmonic detection with tunable diode lasers—two-tone modulation,” Appl. Phys. B 29, 279–285 (1982).
[CrossRef]

D. T. Cassidy, J. Reid, “Atmospheric pressure monitoring of trace gases using tunable diode lasers,” Appl. Opt. 21, 1185–1190 (1982).
[CrossRef] [PubMed]

J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

J. Reid, M. El-Sherbiny, B. K. Garside, E. A. Ballik, “Sensitivity limit of a tunable diode laser spectrometer, with application to the detection of NO2 at the 100-ppt level,” Appl. Opt. 19, 3349–3354 (1980).
[CrossRef] [PubMed]

Riris, H.

Sachse, G. W.

Schaldach, G.

H. Groll, G. Schaldach, H. Berndt, K. Niemax, “Measurement of Cr(III)/Cr(VI) species by wavelength modulation diode laser flame atomic absorption spectrometry,” Spectrochim. Acta Part B 50, 1293–1298 (1995).
[CrossRef]

Schnürer-Patschan, C.

A. Zybin, C. Schnürer-Patschan, K. Niemax, “Wavelength modulation diode laser atomic spectrometry in modulated low-pressure helium plasmas for element-selective detection in gas chromatography.” J. Anal. At. Spectrom. 10, 563–567 (1995).
[CrossRef]

C. Schnürer-Patschan, K. Niemax, “Elemental selective detection of chlorine in capillary gas chromatography by wavelength modulation diode laser atomic absorption spectrometry in a microwave induced plasma,” Spectrochim. Acta Part B 50, 963–969 (1995).
[CrossRef]

H. Groll, C. Schnürer-Patschan, Y. Kuritsyn, K. Niemax, “Wavelength modulation diode laser atomic absorption spectrometry in analytical flames,” Spectrochim. Acta Part B 49, 1463–1472 (1994).
[CrossRef]

C. Schnürer-Patschan, A. Zybin, H. Groll, K. Niemax, “Improvement in detection limit in graphite furnace diode laser atomic absorption spectrometry by wavelength modulation technique.” J. Anal. At. Spectrom. 8, 1103–1107 (1993).
[CrossRef]

A. Zybin, C. Schnürer-Patschan, K. Niemax, “Measurements of C2F4Cl2, CCl4, CHF3, and O2 by wavelength modulated laser absorption spectroscopy of excited Cl, F, and O in a DC discharge applying semiconductor diode lasers,” Spectrochim. Acta Part B 48, 1713–1718 (1993).
[CrossRef]

Schumate, M. S.

Sharpe, S. W.

T. A. Hu, E. L. Chappell, J. T. Munley, S. W. Sharpe, “Improved multipass optics for diode-laser spectroscopy,” Rev. Sci. Instrum. 64, 3380–3383 (1993).
[CrossRef]

Silver, J. A.

Stanton, A. C.

Supplee, J. M.

Tang, C. L.

Wada, O.

N. Kagawa, O. Wada, R. Koga, “Suppression of the etalon fringe in absorption spectrometry with an infrared tunable diode laser,” Opt. Eng. 36, 2586–2592 (1997).
[CrossRef]

Wang, L.-G.

Webster, C. R.

Wells, W. K.

Werle, P.

P. Werle, “Spectroscopic trace gas analysis using semiconductor diode lasers,” Spectrochim. Acta Part A 52, 805–822 (1996).
[CrossRef]

Whittaker, E. A.

Wilson, G. V. H.

G. V. H. Wilson, “Modulation broadening of NMR and ESR lineshapes,” J. Appl. Phys. 34, 3276–3285 (1963).
[CrossRef]

Wu, J.

Zhu, X.

Zybin, A.

V. Liger, A. Zybin, Y. Kuritsyn, K. Niemax, “Diode-laser atomic-absorption spectrometry by the double-beam–double-modulation technique,” Spectrochim. Acta Part B 52, 1125–1138 (1997).
[CrossRef]

A. Zybin, C. Schnürer-Patschan, K. Niemax, “Wavelength modulation diode laser atomic spectrometry in modulated low-pressure helium plasmas for element-selective detection in gas chromatography.” J. Anal. At. Spectrom. 10, 563–567 (1995).
[CrossRef]

A. Zybin, C. Schnürer-Patschan, K. Niemax, “Measurements of C2F4Cl2, CCl4, CHF3, and O2 by wavelength modulated laser absorption spectroscopy of excited Cl, F, and O in a DC discharge applying semiconductor diode lasers,” Spectrochim. Acta Part B 48, 1713–1718 (1993).
[CrossRef]

C. Schnürer-Patschan, A. Zybin, H. Groll, K. Niemax, “Improvement in detection limit in graphite furnace diode laser atomic absorption spectrometry by wavelength modulation technique.” J. Anal. At. Spectrom. 8, 1103–1107 (1993).
[CrossRef]

Appl. Opt.

J. Reid, M. El-Sherbiny, B. K. Garside, E. A. Ballik, “Sensitivity limit of a tunable diode laser spectrometer, with application to the detection of NO2 at the 100-ppt level,” Appl. Opt. 19, 3349–3354 (1980).
[CrossRef] [PubMed]

D. T. Cassidy, J. Reid, “Atmospheric pressure monitoring of trace gases using tunable diode lasers,” Appl. Opt. 21, 1185–1190 (1982).
[CrossRef] [PubMed]

H. Ahlberg, S. Lundqvist, M. S. Schumate, U. Persson, “Analysis of errors caused by optical interference effects in wavelength-diverse CO2 laser long-path systems,” Appl. Opt. 24, 3917–3923 (1985).
[CrossRef]

L.-G. Wang, H. Riris, C. B. Carlisle, T. F. Gallagher, “Comparison of approaches to modulation spectroscopy with GaAlAs semiconductor lasers: application to water vapor,” Appl. Opt. 27, 2071–2077 (1988).
[CrossRef] [PubMed]

J. A. Silver, “Frequency-modulation spectroscopy for trace species detection: theory and comparison among experimental methods,” Appl. Opt. 31, 707–717 (1992).
[CrossRef] [PubMed]

D. S. Bomse, A. C. Stanton, J. A. Silver, “Frequency modulation and wavelength modulation spectroscopies: comparison of experimental methods using a lead-salt diode laser,” Appl. Opt. 31, 718–731 (1992).
[CrossRef] [PubMed]

P. V. Cvijin, W. K. Wells, D. A. Gilmore, J. Wu, D. M. Hunten, G. H. Atkinson, “Fringe pattern suppression in intracavity laser spectroscopy,” Appl. Opt. 31, 5779–5784 (1992).
[CrossRef] [PubMed]

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Other

In deriving Eqs. (1) and (2), we made use of the fact that all odd transmission coefficients are zero, which follows from our choice of reference phase.

Cζ is, in fact, frequency dependent but can, in the interval of frequency over which Eq. (15) takes any appreciable value, be considered constant.

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Figures (4)

Fig. 1
Fig. 1

Lowest even harmonics of the background signal from a frequency-doubled WM diode-laser system plotted as functions of the normalized frequency-doubling center frequency ξ c c for a constant laser center frequency ν c l and a variety of values of κ I : (a) S¯0even and S¯2even and (b) S¯0even and -S¯4even. Curves af on the left-hand axis represent S¯0even for κ I values for which the parameter ∊ takes values of 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0, respectively. Curves gl on the right-hand axis represent, in (a), S¯2even and, in (b), -S¯4even for the same set of values of ∊. It was assumed that the instrumentation was set for the optimum detection of species by frequency-doubled light with a HWHM of 2 GHz, which corresponds to the Doppler width of Ca in an air–acetylene flame. The frequency modulations of the fundamental frequency ν a were therefore taken to be 2.2 and 4.1 GHz for 2f and 4f detection, respectively, as shown in (a) and (b), respectively. It was assumed the κξ had a value of 0.068, which corresponds to the situation for a KNbO3 crystal, according to Ref. 34. This value results in a value of ξ a of 0.15 for 2f detection and of 0.27 for 4f detection.

Fig. 2
Fig. 2

Two lowest even harmonics of the background signal from a frequency-doubled WM diode-laser system plotted as functions of the normalized laser center frequency ξ c l and a variety of values of κ I : (a) S¯0even and S¯2even and (b) S¯0even and -S¯4even. Curves af on the left-hand axis represent S¯0even for κ I values for which the parameter ∊ takes values of 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0, respectively. Curves gl on the right-hand axis represent, in (a), S¯2even and, in (b), -S¯4even for the same set of values of ∊. The S¯neven functions were normalized by the referring of the S¯neven signal to the photodiode signal at the center of the frequency-doubling function, i.e., S(ν c c ). The same values for ν a and ξ a that were used for Fig. 1 were used here. It was assumed that the laser power that corresponded to the intensity on resonance, i.e., I L,0(ν c l ), was 100 mW. Curves are drawn for only those values of ξ c l for which the power of the laser is higher than zero.

Fig. 3
Fig. 3

Two lowest even harmonics of the background signal from a frequency-doubled WM diode-laser system plotted as a function of the parameter ∊ for zero detuning: (a) S¯2even and (b) -S¯4even. Note that the right-hand axis displays -S¯4even. The modulation amplitudes are the same as those shown in Fig. 1.

Fig. 4
Fig. 4

Two lowest even harmonics of the background signal from a frequency-doubled WM diode-laser system plotted as a function of the normalized modulation amplitude ξ a for a value of the parameter ∊ of zero for zero detuning: (a) -S¯2even and (b) S¯4even. Note that the left-hand axis displays -S¯2even.

Tables (4)

Tables Icon

Table 1 Expressions for the Fourier Components of the Square of the Diode-Laser Light with a Linear Associated Intensity Modulation

Tables Icon

Table 2 Coefficients for Eqs. (24) and (A2)

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Table 3 Polynomial g 2k (n) for Eq. (A3)

Tables Icon

Table 4 Coefficients for Eq. (A5)

Equations (44)

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νt=νcl+νa cos2πft,
St=ηIt=ηTνtISHt,
St=ηISHt.
ISHt=ζνtIL2t.
Snνcl, νa=ηISH,nνcl, νa.
Sneven=2-δn0τ0τ Stcos2πnftdt,
Snodd=2τ0τ Stsin2πnftdt.
Snevenνcl, νa=η2m=0n ζn-mevenνcl, νaIL2mevenνcl, νa+2-δn02m=0 ζmevenνcl, νaIL2n+mevenνcl, νa+2-δn02m=0 ζn+mevenνcl, νaIL2mevenνcl, νa,
Snoddνcl, νa=η1-δn02m=1n ζn-mevenνcl, νaIL2moddνcl, νa+m=0 ζmevenνcl, νaIL2n+moddνcl, νa-m=1 ζn+mevenνcl, νaIL2moddνcl, νa,
ILt=IL,0νcl+IL,1νacos2πft+ϕ1,
IL,1νa=κIνa,
Snevenνcl, νa=ηζnevenIL20even+121-δn01+δn1ζn-1even+ζn+1even×IL21even+121-δn01-δn1×1+δn2ζn-2even+δn1ζn+2evenIL22even.
Snoddνcl, νa=η 1-δn021+δn1ζn-1even-ζn+1evenIL21odd+1-δn11+δn2ζn-2even-ζn+2evenIL22odd.
|IL20even|  |IL21even|  |IL22even||IL21odd|  |IL22odd|,
ζν=Cζsin2ξνξ2ν,
ξν=2π νcnFν-nSHνSH,
nFνtnFνcc+nFννν=νcνcl-νcc+νa cos2πft,
ξν(t)=ξdνd+ξaνacos2πft,
ξdνd=2π νcccnFννν=νcc-nSHννν=2νccνcl-νcc=κξνd,
ξaνa=2π νcccnFννν=νcc-nSHννν=2νccνa= κξνa.
ζξd, ξa, t=Cζsin2ξd+ξa cos2πftξd+ξa cos2πft2.
ξd=κξνd=κξνcl-νcc=ξcl-ξcc.
ζnevenξd, ξa  CζFnξdξan,
Fnξd=2-δn02nn!nζξξnξ=ξd=2-δn,02nξdnAnsin2ξdξd2 + Bn cosξdsinξdξd+Cn cos2ξd,
|ζ0even|  |ζ2even|  |ζ4even|  |ζ6even|,
S0evenξd, ξa=ηζ0evenIL20even+12 ζ1evenIL21even+12 ζ2evenIL22even,
S1evenξd, ξa=ηζ1evenIL20even+ζ0evenIL21even+12 ζ1evenIL22even,
Sn,n2evenξd, ξa=ηζnevenIL20even+12 ζn-1evenIL21even+1+δn22 ζn-2evenIL22even.
Snevenξd, ξaηCζΓnξd, ξaξanIL,02νcl=Γnξd, ξaξanSνcl,
Γ0ξd, ξa=Fn-Fn+1ξa2+1+δn24 Fn+2ξa4+12 Fnξa22,
Γn,n2ξd, ξa=Fn-Fn-1+1+δn24 Fn-2+12 Fnξa22
Γ0ξd, ξa=anfn-an+1fn+1ξa2ξd+1+δn24 an+2fn+2ξa2+an2 fnξa22,
Γn,n2ξd, ξa=anfn-an-1fn-1ξd+1+δn24 an-2fn-2+an2 fnξa22
=κIκξIL,0νcl.
S¯nevenξd, ξa=Snevenξd, ξaSνclΓnξd, ξaξan.
S¯2evenξd, ξa-161-32ξa2,
S¯4evenξd, ξa11801-152 2ξa4,
S¯6evenξd, ξa-1100801-142ξa6.
|S2even|  |S4even|  |S6even|.
ζξd, ξa, tn=0 ξnξd, ξacosn2πft,
ζnξd, ξa=CζξaξdnAnsin2ξdξd2+Bn cosξdsinξdξd+Cn cos2ξd.
ζnevenξd, ξa=2-δn02n×k=0kmaxg2knk!22k ζn+2kξd, ξa,
ζneven=anfnξd, ξaξanξdnCζ,
fnξd, ξa=1-bnξa2-cn-dnξa2ξd2.

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